If it is the ring gear, you might take a die grinder and attempt to taper the damaged teeth again to allow a smoother engagement (for a time at least). Remember, starter engagement location on the ring gear depends on where the engine last stopped. If the engine stopped with the damaged teeth exposed to the starter, the result in the grinding noise. If the ring gear is not replaced, you can probably go a while before it becomes a real problem and not engage at all. The symptoms will only get worse with each grinding startup.
If the time comes that the starter fails to engage the ring gear, you can rotate the crank by hand about 15 degrees to expose a non-damaged set off teeth to the starter. Given this is an automatic; you will need to use a socket wrench on the front crank pulley. Or sometimes you can rotate the alternator pulley or whatever other accessories there are exposed. Just stating the last part so you understand the ring gear is not totally damaged, just certain spots. Might help you if your stranded somewhere and the starter will only make those grinding noises.
If you are interested in the details of how the ring is setup and what it takes to change it, go to the link below and find the manual for your Generation of car.
http://oregonstate.edu/~tongt/camry